Question

select the correct answer.
a boat is anchored in the water. the anchor lies at point a. at low tide, the boat is floating 20 feet above the seafloor and is a horizontal distance of 40 feet away from its anchor. at high tide, the boat is a horizontal distance of 35 feet away from its anchor.
low tide high tide
20 ft? ft
40 ft 35 ft
a a
approximately how high is the boat floating above the seafloor at high tide? assume the anchor rope remains tight, without any slack.
a. 35.7 ft
b. 22.5 ft
c. 15.6 ft
d. 27.8 ft

Explanation:

Step1: Calculate rope length (low tide)

Use Pythagorean theorem: $c = \sqrt{a^2 + b^2}$

$$ c = \sqrt{20^2 + 40^2} = \sqrt{400 + 1600} = \sqrt{2000} $$

Step2: Solve for high tide height

Let height = $h$. Use Pythagorean theorem: $h = \sqrt{c^2 - 35^2}$

$$ h = \sqrt{2000 - 1225} = \sqrt{775} \approx 27.8 $$

Answer:

D. 27.8 ft